x^2-31.25x+244.140625=242.890625

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Solution for x^2-31.25x+244.140625=242.890625 equation:


Simplifying
x2 + -31.25x + 244.140625 = 242.890625

Reorder the terms:
244.140625 + -31.25x + x2 = 242.890625

Solving
244.140625 + -31.25x + x2 = 242.890625

Solving for variable 'x'.

Reorder the terms:
244.140625 + -242.890625 + -31.25x + x2 = 242.890625 + -242.890625

Combine like terms: 244.140625 + -242.890625 = 1.25
1.25 + -31.25x + x2 = 242.890625 + -242.890625

Combine like terms: 242.890625 + -242.890625 = 0.000000
1.25 + -31.25x + x2 = 0.000000

Begin completing the square.

Move the constant term to the right:

Add '-1.25' to each side of the equation.
1.25 + -31.25x + -1.25 + x2 = 0.000000 + -1.25

Reorder the terms:
1.25 + -1.25 + -31.25x + x2 = 0.000000 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + -31.25x + x2 = 0.000000 + -1.25
-31.25x + x2 = 0.000000 + -1.25

Combine like terms: 0.000000 + -1.25 = -1.25
-31.25x + x2 = -1.25

The x term is -31.25x.  Take half its coefficient (-15.625).
Square it (244.140625) and add it to both sides.

Add '244.140625' to each side of the equation.
-31.25x + 244.140625 + x2 = -1.25 + 244.140625

Reorder the terms:
244.140625 + -31.25x + x2 = -1.25 + 244.140625

Combine like terms: -1.25 + 244.140625 = 242.890625
244.140625 + -31.25x + x2 = 242.890625

Factor a perfect square on the left side:
(x + -15.625)(x + -15.625) = 242.890625

Calculate the square root of the right side: 15.584948669

Break this problem into two subproblems by setting 
(x + -15.625) equal to 15.584948669 and -15.584948669.


Subproblem 1
x + -15.625 = 15.584948669

Simplifying
x + -15.625 = 15.584948669

Reorder the terms:
-15.625 + x = 15.584948669

Solving
-15.625 + x = 15.584948669

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '15.625' to each side of the equation.
-15.625 + 15.625 + x = 15.584948669 + 15.625

Combine like terms: -15.625 + 15.625 = 0.000
0.000 + x = 15.584948669 + 15.625
x = 15.584948669 + 15.625

Combine like terms: 15.584948669 + 15.625 = 31.209948669
x = 31.209948669

Simplifying
x = 31.209948669


Subproblem 2
x + -15.625 = -15.584948669

Simplifying
x + -15.625 = -15.584948669

Reorder the terms:
-15.625 + x = -15.584948669

Solving
-15.625 + x = -15.584948669

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '15.625' to each side of the equation.
-15.625 + 15.625 + x = -15.584948669 + 15.625

Combine like terms: -15.625 + 15.625 = 0.000
0.000 + x = -15.584948669 + 15.625
x = -15.584948669 + 15.625

Combine like terms: -15.584948669 + 15.625 = 0.040051331
x = 0.040051331

Simplifying
x = 0.040051331


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {31.209948669, 0.040051331}

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